Question: Let f be a complex-valued function defined on an open set ? that is symmetric with respect to the real line, that is, z E

Let f be a complex-valued function defined on an open set ? that is symmetric with respect to the real line, that is, z E 2 implies Z E 2. (Examples are C and D(x, r) where r E R.) Set g(z) = f(2), and show that if f is analytic on & then g is also analytic on 1

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